Problem Solving

Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 15 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?

A. 10.5
B. 15
C. 25.5
D. 30
E. 60

The OA is A.

Experts, what are the equations I should set to solve this PS question? I am a little confused. Thanks in advanced.

M7MBA wrote:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 15 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?

A. 10.5
B. 15
C. 25.5
D. 30
E. 60

The OA is A.

Experts, what are the equations I should set to solve this PS question? I am a little confused. Thanks in advanced.

If she walks to work at 3mph, and she lives 1.5 miles away, it will take her 3t = 1.5 --> t = .5 hours, or 30 minutes to walk. We know it takes her 15 more minutes to walk than to take the train, so it must take her 30 -15 = 15 minutes to take the train.

If she weren't waiting for an additional x minutes when taking the train, her trip would take 20t = 1.5 --> t = 1.5/20 = 4.5/60 hours = 4.5 minutes. So it she would have taken 4.5 minutes without having to wait, but it actually takes her 15 minutes, then she must have been waiting for 15 - 4.5 = 10.5 minutes. The answer is A